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Question

In the expansion of (713+1119)6561

A
There are exactly 730 rational terms
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B
There are exactly 5831 irrational terms
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C
The term which involves greatest binomial coefficients is irrational
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D
The term which involves greatest binomial coefficients is rational
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Solution

The correct option is C The term which involves greatest binomial coefficients is irrational
General term is 6561Cr(76561r3)11r9.
Terms will be rational if r is a multiple of 9.
r=0,9,18,27,....,6561.
Now 6561=0+(n1)9n=730
Hence, there are 730 rational terms. The greatest binomial coefficients are 6561C656112 and 6561C6561+12
6561C3280 and 6561C3281
Now, 3280 are 3281 are not a multiple of 3; hence, both terms involving greatest binomial coefficients are irrational.

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